A nonlinear eigenvalue problem
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We reduce the problem of the zeros of an entire function related to the Painlevé I equation to the eigenvalue problem for the Dirichlet problem for a fourth-order bilinear equation. In a simplified case, this problem reduces to the problem of the position of the zeros of theta functions. We then apply the developed general method to the inverse scattering problem.
Keywordsentire function Painlevé transcendent inverse scattering problem
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